@MISC{New_quark-antiquarkcondensates, author = {Kevin Cahill New and Kevin Cahill}, title = {Quark-Antiquark Condensates Break Chiral Symmetry}, year = {} }

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Abstract

In the physical vacuum of QCD, the energy density of lightquark fields strongly coupled to slowly varying gluon fields can be negative. The states that drive this energy density lowest are condensates of pairs of quarks and antiquarks of nearly opposite momenta. These quark-antiquark condensates break chiral symmetry. August 23, 2001 # kevin@kevin.phys.unm.edu http://kevin.phys.unm.edu/kevin/ 1 The QCD Vacuum The principal idea of this paper is that the energy density of strongly coupled light quarks can be negative and that this feature of QCD breaks chiral symmetry. The hamiltonian H q of the u, d, and s quarks H q = # f=u,d,s # d 3 x # f # ## # #- ig# 0 A 0a # a 2 - ig## # A a # a 2 +m f # # f (1) can assume large negative mean values due to the term -g # d 3 x # J a # A a when the gauge field # A a varies slowly with a modulus | # A a | that exceeds m u /g by a su#cient margin [1]. For nearly constant gauge fields # A a , the states that drive the energy lowest are condensates [2] of pairs of light quarks and antiquarks of opposite momenta; in such pairs the color charges cancel, but the color currents add. When g| # A a | # m d , the u and d quarks play very similar roles, and ss pairs become important when g| # A a | # m s . If the gauge fields are not only slowly varying but also essentially abelian, in the sense that gf abc A b A c # is small (e.g., because A a (x) # C a (x)V (x)), then the energy of the gauge fields is also small. Suppose that an essentially abelian gauge field, e.g., | # A 8 |, is nearly constant over a sphere of radius R beyond which it decreases with increasing radius, falling to zero when R = L. Then its energy density is practically zero inside the sphere of radius R, is zero ...